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No.  112 


Health,  Education,  Recreation 


THE  RELATION  BETWEEN  ENTERING 

AGE  AND  SUBSEQUENT  PROGRESS 

AMONG  SCHOOL  CHILDREN 


LEONARD  P.  AYRES,  Ph.D. 


'JLIllO 


iv;  ■' 


Reprinted  from 

Education,  February,  1912,  by  the 

Department  of  Child  Hygiene 

Russell  Sage  Foundation 

400  Metropolitan  Tower,  New  York  City 


1-12-16 


L  \5 


The  Relation  Between  Entering  Age  and  Sub- 
sequent Progress  Among  School  Children 

Every  parent  and  teacher  desires  an  answer  to  the  perennially 
important  question  "What  is  the  best  age  at  which  to  send  a 
child  to  school?"  Those  whose  interest  becomes  active  usually 
seek  an  answer  through  questioning  the  recognized  authorities 
in  pedagogy  and  child  hygiene.  The  experience  of  such  seekers 
after  knowledge  is  like  that  of  Omar  of  old,  for  they  eagerly 
frequenti  doctor  and  pedagog  and  hear  great  argument. 

In  general,  the  pedagog  solves  the  problem  through  the  proc- 
esses of  near-philosophic  induction,  and  decides  that  the  best 
entering  age  is  relatively  low,  while  the  physician  arrives  at  his 
conclusion  through  the  simple  method  of  dogmatic  assertion, 
and  declares  that  the  best  beginning  age  is  a  relatively  high  one. 
The  discussion  on  both  sides  is  invariably  lively  and  protracted, 
for  the  exponents  of  the  two  theories  enjoy  the  great  advantage 
of  being  entirely  unhampered  by  facts.  The  result  is  that, 
again  like  Omar  of  old,  the  seeker  after  knowledge  comes  out 
of  the  same  door  wherein,  he  went. 

In  England,  an  important  contribution  toward  the  solution  of 
the  problem  has  recently  been  made  by  Inspector  W.  H.  Winch, 
who  has  published  the  results  of  his  extensive  and  careful  re- 
searches in  an  excellent  monograph  entitled,  "When  should  a 
Child  Begin  School.?"  Unfortunately,  this  study  is  of  only  limited 
value  in  its  application  to  conditions  in  America  for  the  reason 
that  children  still  commonly  begin  school  in  England  at  the  age 
of  three  or  four  years,  and  the  question  at  issue  is  whether 
or  not  this  practice  produces  beneficial  results.  In  the  United 
States,  on  the  other  hand,  the  age  of  five  is  commonly  the  lowest 
school  age,  while  in  some  states  the  lower  limit  is  fixed  by  law 
at  six.  What  the  American  parent  and  teacher  want  to  know 
is  which  is  in  general  the  best  entering  age  under  present  con- 
ditions in  our  school  systems. 

The  present  article  presents  data  gathered  by  the  writer 
which  bear  on  one  phase  of  this  problem — the  relative  subse- 

3 


quent  progress  through  the  grades  made  by  children  who  enter 
school  at  each  of  the  ages  from  five  to  ten  years  inclusive. 

In  1908,  the  writer  conducted  an  investigation  for  the  Board 
of  Education  of  New  York  City  in  which  a  study  was  made 
of  the  school  histories  of  some  20,000  children  in  fifteen  schools 
in  Manhattan.  Among  these  was  a  group  of  257  pupils  in  the 
eighth  grades,  who  were  about  to  graduate,  and  whose  entire 
school  histories  from  the  date  of  first  entering  were  intact  and 
available.  The  number  of  children  in  each  entering  age  group 
and  the  time  taken  to  complete  the  course  were  as  follows: — 

I.    AGE  AT  ENTERING  AND  TIME  IN  SCHOOL  OF  257  EIGHTH 
GRADE  PUPILS  IN  NEW  YORK  CITY,  1908 

Average  Number 
Age  at  of  Years  to  Complete 

Entering  Number  Eight  Grades 

5 64  8.9 

6 113  8.6 

7 54  8.4 

8 19  8.2 

9 7  7-2 

The  figures  show  a  steady  but  slight  falling  off  in  the  amount 
of  time  required  by  the  children  of  each  advancing  age  group  to 
complete  the  course.  This  decrease  is  so  sm.all  that  it  lends  no 
support  whatever  to  the  prevalent  opinion  that  the  child  entering 
school  late  will  make  such  rapid  progress  as  easily  to  catch  up 
with  the  children  who  entered  two  or  three  years  earlier. 

A  second  study  of  the  histories  of  school  children  was  con- 
ducted for  the  New  York  Board  of  Education  in  1909.  This 
investigation  included  the  records  of  all  the  children  who  were 
in  the  graduating  classes  throughout  the  entire  city  in  June  of 
that  year.  There  were  16,000  of  them,  and  the  investigation 
covered  their  complete  school  records  from  their  entry  into  the 
Kindergarten  or  first  grade  through  to  the  completion  of  the 
eighth  grade. 

For  the  purpose  of  studying  the  influence  of  entering  ages 
upon  subsequent  progress,  only  records  of  children  who  had  en- 
tered in  the  first  grade  and  completed  the  eighth  were  tabulated. 
All  those  of  children  entering  in  grades  beyond  the  first  were 
discarded,  as  were  those  in  which  there  was  any  question  as  to  the 
accuracy  of  the  data.  This  left  a  total  of  11,185  cases.  The 
ages  at  starting  varied  from  five  to  twelve  years,  inclusive,  while 
the  time  for  completing  the  course  ranged  from  five  and  one-half 


to  thirteen  and  one-half  years.  The  following  table  shows  the 
number  of  children  in  each  entering  age  group,  together  with  the 
median  time  required  to  complete  the  course: — 

II.  AGE  AT  ENTERING  AND  TIME  TO  COMPLETE  EIGHT  GRADES 
OF  11,185  CHILDREN  IN  NEW  YORK  CITY,  1909 

Median  Number 
Age  at  of  Years  to  Complete 

Entering  Number  Eight  Grades 

5 1521  8.2 

6 5828  8.1 

7 2936  8.0 

8 721  7.9 

9 142  7-4 

10 26  6.9 

II 9  6.6 

12 2  6.3 

The  lesson  clearly  taught  by  the  table  is  that  children  entering 
school  at  the  advanced  ages  made  more  rapid  progress  than  did 
those  who  began  earlier,  but  that  the  difference  is  slight.  The 
child  who  entered  at  the  age  of  six  gained  one  school  month  in 
the  course  of  eight  years  over  his  companion  who  began  at  five. 
The  one  who  began  at  seven  gained  one  month  over  the  one 
who  started  at  six,  and  the  child  entering  at  eight  gained  one 
month  over  the  one  starting  at  seven. 

In  the  cases  of  the  children  who  started  at  from  nine  to  twelve 
years  of  age,  the  gains  were  greater,  amounting  to  from  three  to 
five  months  for  each  advancing  age.  Nevertheless,  these  figures 
again  expose  the  fallacy  of  the  common  assertion  that  the  child 
entering  late  easily  catches  up  with  the  one  who  begins  early. 

The  third  set  of  data  throwing  light  on  the  question  of  entering 
ages  is  much  more  significant  than  those  already  hastily  reviewed. 
In  the  spring  of  191 1  the  Division  of  Education  of  the  Sage 
Foundation  undertook  a  co-operative  investigation  with  the 
superintendents  of  a  number  of  city  school  systems  for  the  purpose 
of  studying  factors  affecting  the  progress  of  school  children. 

Data  of  this  investigation  covering  the  progress  and  age 
records  of  206,495  children  in  29  cities  have  been  tabulated. 
Of  this  number  13,867  are  the  records  of  the  entire  membership 
of  the  eighth  grades  of  these  twenty-nine  cities  at  the  close  of 
the  school  year  1910-11.  The  number  of  years  required  to  com- 
plete the  eight  grades  varies  from  three  to  twelve,  while  the 
entering  ages  range  from  five  to  fourteen.  The  number  of  chil- 
dren in  each  entering  age  group,  together  with  the  median  time 


required  to  complete  the  eight  grades,  is  shown  in  the  following 
table:— 

III.  AGE  AT  STARTING  AND  TIME  TO  COMPLETE  EIGHT  GRADES 

OF  13,867  CHILDREN  IN  THE  GRADUATING  CLASSES 
OF  29  CITIES  JUNE,  1911 

Age  at  Median  Number  of  Years  to 

Entering  Number  Complete  Eight  Grades 

5 2663  8.7 

6 6050  8.5 

7 3653  8-2 

.     8 1151  7-8 

9 255  7-2 

10 58  6.3 

II 22 

12 9 

13 3 

14 3 

These  figures  closely  resemble  the  two  foregoing  series.  They 
show  that  the  children  who  enter  at  advanced  ages  gain  a  little 
on  those  who  enter  early,  and  that  this  gain  becomes  greater  as 
the  upper  ages  are  reached.  They  again  show  that  this  gain  is 
not  enough  to  enable  the  late  entering  child  to  catch  up  with 
the  one  who  enters  early. 

Rapid,  Normal  and  Slow  Progress 
In  studying  the  records  of  the  children  in  the  twenty-nine 
cities,  a  division  into  three  progress  groups  was  made  in  which 
those  who  had  taken  more  than  eight  years  to  complete  the 
eight  grades  were  designated  as  slow,  those  who  had  taken  just 
eight  years  as  normal,  and  those  getting  through  in  less  than 
eight  years  were  termed  rapid.  The  results  of  this  tabulation 
show  that  the  children  of  each  entering  age  were  divided  among 
these  three  progress  groups  as  follows: 

IV.  PROGRESS  CLASSIFICATION  OF  13,867  CHILDREN  IN  THE 
EIGHTH  GRADES  OF  29  CITIES,  ACCORDING  TO  PER 
CENT  RAPID,  NORMAL,  AND  SLOW  IN  EACH  ENTERING 
AGE  GROUP 

Age  at  Per  Cent  Per  Cent  Per  Cent 

Entering  Rapid  Normal  Slow 

5 10  58  32 

6 27  52  21 

7 40  45  15 

8 59  33  8 

9 81  17  2 

10 98  2 

II 100 

12 100 

13 100 

14 100 


7 

The  table  shows  that  the  per  cent  of  slow  pupils  is  greatest 
among  the  children  entering  at  five,  and  that  the  pupils  making 
rapid  progress  are  those  who  entered  at  the  advanced  ages.  This 
brings  up  a  difficult  question.  Is  the  best  entering  age  the  one 
which  results  in  the  greatest  proportion  of  rapid  pupils,  the 
smallest  proportion  of  slow  pupils,  the  largest  proportion  of  normal 
pupils,  or  the  most  equal  balance  between  the  three  groups? 

The  writer  is  inclined  to  the  opinion  that  so  far  as  the  present 
griteria  are  concerned,  the  best  entering  age  is  the  one  that 
results  in  a  large  proportion  of  normal  pupils,  combined  with 
the  most  equal  balance  between  the  rapid  and  slow  groups.  In 
the  present  case,  this  is  the  entering  age  of  six,  which  results  in 
fifty-two  per  cent  of  the  pupils  making  normal  progress,  twenty- 
seven  per  cent  rapid  progress,  and  twenty-one  per  cent  slow. 

Division  into  Young,  Normal  and  Over-age  Groups 
A  second  tabulation  of  the  data  was  made  which  classified 
the  same  children  according  to  their  ages.  Here  the  common 
standard  was  followed  which  considers  a  fourteen-year-old  child 
in  the  eighth  grade  as  of  normal  age,  one  younger  as  below  nor- 
mal age,  and  one  older  as  above  normal  age.  This  classification 
gave  the  following  results: — 

V.  AGE  CLASSIFICATION  OF  13,867  CHILDREN  IN  THE  EIGHTH 
GRADES  OF  29  CITIES,  ACCORDING  TO  PER  CENT  YOUNG, 
NORMAL,  AND  OVER-AGE  FOR  EACH  ENTERING  AGE  GROUP 

Age  at  Per  Cent  Per  Cent  Per  Cent 

Entering  Young  Normal  Over-Age 

5 67  25  8 

6 27  52  21 

7 8  33  59 

8 3  14  83 

9 2  7  91 

10 2  10  88 

II 5  95 

12 . .  100 

13 . .  100 

14 . .  100 

Here  the  results  are  just  the  opposite  from  those  of  the  progress 
classification.  The  best  showing  is  made  by  the  children  who 
entered  at  the  lower  ages  and  the  worst  ones  by  those  who 
entered  late.  It  resembles  the  preceding  table  however,  in  that 
the  entering  age  of  six  is  the  one  which  results  in  combining  the 
greatest  proportion  of  normal  pupils  with  the  most  equal  balance 
between  the  young  and  over-age  groups. 


8 

The  reason  why  the  children  of  the  lower  age  groups  make 
the  best  showing  becomes  apparent  at  once  if  we  refer  to  the 
table  showing  the  median  number  of  years  required  by  these 
same  children  to  complete  the  course  and  compute  their  ages 
at  graduation,  as  follows: 

VI.    AGE  AT  ENTERING,  YEARS  TO  COMPLETE  COURSE  AND 

AGE  AT  GRADUATION.     BASED  ON  RECORDS  OF  13,867 

CHILDREN  IN  29  CITIES 

Median  Number 
Age  at  of  Years  to  Age  at 

Entering  Complete  Eight  Grades  Graduation 

5 8.7  13.7 

6 8.5  14.5 

7 8.2  15.2 

8 7.8  15-8 

9 7.2  16.2 

10 6.3  16.3 

A  glance  at  the  figures  of  the  last  column  shows  that  the 
children  of  all  but  the  two  lowest  entering  age  groups  are  above 
the  normal  age  for  their  grades.  Moreover,  nearly  all  the 
children  who  were  eight  years  old  or  older  at  the  time  of  begin- 
ning school  remained  above  normal  age  for  their  grades  during 
their  entire  school  course.  So  far  as  age  went,  they  were  misfits 
during  the  entire  elementary  school  period. 

Relative  Homogeneity  of  Entering  Age  Groups 
Another  test  which  may  be  applied  to  the  data  for  the  several 
entering  age  groups  is  one  to  tell  us  which  entering  age  results 
in  the  greatest  probability  that  the  child  will  continue  through 
the  course  with  his  companions  of  the  same  age  with  whom  he 
entered  the  first  grade.  We  may  answer  this  question  by  find- 
ing the  probable  error  for  the  progress  data  of  each  entering 
age  group.  That  is  to  say,  we  may  find  which  group  is  most 
homogeneous  as  to  progress  by  finding  the  range  in  the  distri- 
bution of  the  progress  figures,  which  will  include  that  half  of  the 
cases  most  closely  clustered  about  the  median  point.  The  group 
in  which  the  range  is  least  is  the  one  having  the  greatest  homo- 
geneity. The  probable  errors  for  the  several  entering  age  groups 
are  as  follows: — 

Entering  Probable  Error 

Age  in  Years 

5 1-05 

6 i.oi 

7 • 1-24 

8 1.28 

9 1-46 

10 1.27 


Once  more,  the  age  of  six  is  the  one  making  the  best  showing. 
As  the  probable  error  for  this  group  is  the  smallest,  the  group  is 
the  most  homogeneous. 

To  summarize: — 

1.  The  results  of  these  three  studies  of  the  school  histories 
of  more  than  25,000  school  children  who  have  completed 
the  elementary  course  indicate  that  children  entering  at 
advanced  ages  subsequently  make  more  rapid  progress  than 
those  who  enter  younger. 

2.  The  subsequent  progress  of  children  entering  at  the 
more  advanced  ages  is  slightly  more  rapid  than  that  of  those 
entering  at  the  lower  ages,  but  it  is  not  sufficient  to  enable 
the  child  to  overtake  in  the  school  course  the  child  who 
entered  younger. 

3.  The  entering  age  of  six  is  the  one  which  makes  the  best 
showing  with  respect  to  resulting  in  a  large  proportion  of 
the  children  making  normal  progress  and  nearly  even  bal- 
ance between  the  rapid  and  slow  groups. 

4.  The  entering  age  of  six  is  the  one  which  makes  the  best 
showing  with  respect  to  resulting  in  the  largest  proportion 
of  the  children  finishing  the  course  at  normal  age  and  a 
nearly  even  balance  between  the  under-age  and  over-age 
groups. 

5.  The  entering  age  of  six  furnishes  the  most  homogeneous 
group,  judged  on  the  basis  of  subsequent  progress. 


It  must  be  remembered  that  the  foregoing  data  and  conclusions 
bear  only  on  one  phase  of  this  problem,  and  that  a  phase  which  is 
measured  only  in  terms  of  time.  They  do  not  furnish  a  complete 
answer  to  the  question  "Which  is  the  best  entering  age?"  nor 
do  they  indicate  what  results  might  be  found  in  a  system  where 
each  child's  progress  was  directly  and  entirely  dependent  on  his 
capacity  and  unaffected  by  more  or  less  arbitrary  systems  of 
promotion.  They  do,  however,  throw  considerable  new  light 
on  the  question  of  the  relation  between  entering  age  and  progress 
under  present  conditions  in  city  school  systems,  and  their  indi- 
cations point  strongly  to  the  age  of  six  as  the  one  which,  in  general, 
gives  the  best  progress  results. 


Some   Pamphlets    on  Measurements    in    Education 

Issued  by  the  Department  of  Child  Hygiene, 

Russell  Sage  Foundation 


No.  6i.  The    Relation    of    Physical    Defects    to    School 
Progress.     Leonard  P.  Ayres,  Ph.D. 
A  statistical  study  based  on  7608  cases.     9  pp. 

No.  77.  Why  250,000  Children  Quit  School. 
Luther  H.  Gulick,  M.D. 
An  account  of  an  investigation  of  the  reasons  why 
so  large  a  proportion  of  children  fail  to  complete  the 
school  course.     30  pp. 

No.  94.  Measurements  as  Applied  to  School  Hygiene. 
Luther  H.  Gulick,  M.D. 
A    presentation   of   the    need    for   measuring   the 
results  of  our  present  school  processes.     7  pp. 

No.  107.  The  Binet-Simon  Measuring  Scale  for  Intelli- 
gence:   Some  Criticisms  and  Suggestions. 
Leonard  P.  Ayres,  Ph.D. 
A  critical  study  of  these  tests  as  used  in  American 
schools,  and  suggestions  as  to  their  adaptation  to 
our  conditions. 

No.  108.  The  Identification  of  the  Misfit  Child. 
Leonard  P.  Ayres,  Ph.D. 
Data  from  a  study  of  the  age  and  progress  records 
of  school  children  in  twenty-nine  cities. 

No.  no.  The  Relative  Responsibility  of  School  and  So- 
ciety FOR  THE  Over-age  Child. 
Leonard  P.  Ayres,  Ph.D. 
Data  from  a  study  of  the  age  and  progress  records 
of  school  children  in  twenty-nine  cities,  showing  the 
number  of  children  over-age  because  of  late  entrance, 
slow  progress,  and  both  causes  combined. 


No.  57.  The  Department  Bulletin. 

Contains  an  account  of  the  Activities  and  a  list 
of  Publications.     Mailed  free  upon  request. 


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